Today I had the common ajax spin issue with a client, running contact-form-7 version 2.4.1. After a few hours of checking into it, apparently an issue with either permalinks or page coding, but I'm not entirely sure. Nothing looked janky.
My fix was to copy the original contact-page HTML directly into the "contact form 7 page" via the plugin.
Then I deleted the original contact-page, created a new contact page only adding the shortcode to activate contact form 7.
Tested it and saw the pretty little green box message sent box!
We have many other clients which use contact 7 plugin latest version too on WP 3.01, I did a quick check on several and all were fine.
It's a mystery as to why this problem occurs for some, this plugin is one of the most stable and easy to use out there.
Hope this fix helps,